7th Grade Math Chapter 6 Percents

Transcription

1 7th Grade Math Chapter 6 Percents Name: Period: Common Core State Standards CC.7.EE.2 - Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. CC.7.EE.3 - Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. CC.7.RP.3 - Use proportional relationships to solve multistep ratio and percent problems. Scope and Sequence Day 1 Lesson 6-1 Day 8 Lesson 6-5 Day 2 Lesson 6-2 Day 9 Lesson 6-6 Day 3 Lesson 6-3 Day 10 Lesson 6-6 Day 4 Quiz Day 11 Tech Lab Day 5 Lesson 6-4 Day 12 Review Day 1 Day 6 Lesson 6-4 Day 13 Review Day 2 Day 7 Lesson 6-5 Day 14 Test 1

2 IXL Modules SMART Score of 80 is required Due on Review Day 1 Lesson 1 7.L.1 What percentage is illustrated? 7.L.2 Convert between percents, fractions and decimals 7.L.3 Compare percents to fractions and decimals 7.H.5 Put rational numbers in order Lesson 2 7.L.4 Estimate percents of numbers 7.L.5 Percents of numbers and money amounts 7.L.6 Percents of numbers: word problems 7.M.6 Percent of a number: tax, discount and more 7.M.7 Find the percent: tax, discount and more 7.M.8 Sale prices: find the original price 7.M.9 Multi-step problems with percents 7.M.10 Estimate tips Lesson 4 7.L.9 Percent of change 7.L.10 Percent of change: word problems Lesson 5 7.L.7 Solve percent equations 7.L.8 Solve percent equations: word problems 2

3 Lesson 6-1 Fractions, Decimals and Percents Warm-Up Examples: Writing Decimals as Percents Write 0.7 as a percent. Method 1: Method 2: Write 0.3 as a percent. Method 1: Method 2: 3

4 Examples: Writing Fractions as Decimals 5 Write 3 as a percent. Method 1: Method 2: 3 Write 5 as a percent. Method 1: Method 2: Examples: Ordering Rational Numbers 3 4 Order 17%, 0.25, 4, 0.1, 5 and 20% from least to greatest. 4

5 1 3 Order 12%, 0.20, 2, 0.8, 4 and 40% from least to greatest. Examples: Choosing a Method of Computation Decide whether using pencil and paper, mental math or a calculator is most useful when solving the following problems. Then solve. If 27 out of 50 people have the newspaper delivered to their home, what percent of these people have the newspaper delivered to their home? If 10 out of 50 students have blue backpacks, what percent of the students have blue backpacks. 5

6 Lesson 6-2 Estimating with Percents Warm-Up Examples: Using Fractions to Estimate Percents Use a fraction to estimate 27% of 63. Use a fraction to estimate 48% of 91. Examples: Consumer Math Application Tara s T s is offering 2 T-shirts for $16, while Good-T s is running their buy one get one for $9.99, get one for half price sale. Which store offers the better deal? 6

7 Billy s Office Supply Store is offering 25% off a leather notebook, originally priced at $9.75. K s Office Supply Store offers the same notebook, not on sale, at $7.00. Which store offers the better deal? Examples: Estimating with Simple Percents Use 1% or 10% to estimate the percent of each number. 4% of 18 29% of 80 5% of 14 7

8 21% of 60 Examples: Using Fractions to Estimate Percents Use a fraction to estimate 27% of 63. Use a fraction to estimate 48% of 91. Examples: Consumer Math Application Tim spent $58 on dinner for his family. About how much money should he leave for a 15% tip? Amanda spent $12 on a hair cut. About how much money should she leave for a 15% tip? 8

9 Lesson 6-3 Using Properties with Rational Numbers Warm-Up Examples: Writing Equivalent Expressions An art teacher pays $13.89 for one box of watercolor brushes. She buys 6 boxes in March and 5 boxes in April. Use the Distributive Property to write equivalent expressions showing two ways to calculate the total cost of the watercolor boxes. Method 1: Method 2: Jamie earns $8.75 per hour. Last week she worked 15 hours and next week she will work 20 hours. Use the Distributive Property to write equivalent expressions showing two ways to calculate how much money she earned. Method 1: Method 2: 9

10 Examples: Writing Equivalent Expressions Write an equivalent equation that does not contain fractions. Then solve the equation. Examples: Construction Application The soccer team uses a liter container to take water to games. The team manager fills 0.75 liter bottles from this. He has used 22.5 liters. How many more 0.75 liter bottles can he fill before he runs out of water? Write and solve an equivalent equation without decimals....if the soccer team uses a 42.5 liter container, about how many 0.75 liter bottles can the manager fill before he runs out of water? 10

11 Lesson 6-4 Percent of Change Warm-Up Percent of change is the amount, stated as a percent, that a number or. If the amount goes, it is a percent of increase. If the amount goes, it is a percent of decrease. Examples: Finding Percent of Change Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. 65 is decreased to is increased to is decreased to 45 11

12 37 is increased to 56 Examples: Using Percent of Change The regular price of a bicycle helmet is $ It is on sale for 20% off. What is the sale price? The regular price of a computer game is $ It is on sale for 15% off. What is the sale price? Examples: Business Application A boutique buys hand-painted T-Shirts for $12.60 each and sells them at a 110% increase in price. What is the retail price of the T-shirts? William makes T-shirts for $7.00 each and sells them after a price increase of 125%. What is the retail price of the T-shirts? 12

13 Lesson 6-5 Applications of Percents Warm-Up A commission is a paid to a person who makes a. The commission rate is the of the that is paid to the salesperson. Commission Rate x Sales = Commission Examples: Multiplying by Percents to Find Commission Amounts A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month? A car sales agent is paid a monthly salary of $700 plus commission. Last month she sold one sports car for $50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month? 13

14 Sales tax is the tax on the sale of an or. It is a of the purchase price and is collected by the. Examples: Multiplying by Percents to Find Sales Tax Amounts If the sales tax rate is 6.75%, how much tax would Adrian pay if he bought two CDs at $16.99 each and one DVD for $36.29? Amy stays in a hotel for $45 per night. She stays for two nights and pays a sales tax of 13%. How much tax did she pay? Examples: Using Proportions to Find the Percent of Earnings Anna earns $1,500 monthly. Of that, $ is withheld for Social Security and Medicare. What percent of Anna s earnings are withheld for Social Security and Medicare? BJ earns $2,500 monthly. Of that, $500 is withheld for income tax. What percent of BJ s earnings are withheld for income tax? 14

15 Examples: Dividing by Percents to Find Total Sales A furniture sales associate earned $960 in commission in May. If his commission is 12% of sales, how much were his sales in May? A sales associate earned $770 in commission in May. If his commission is 7% of sales, how much were sales in May? 15

16 Lesson 6-6 Percent of Change Warm-Up Interest is the amount of money charged for or money. Simple interest is one type of for the use of money. Examples: Finding Interest and Total Payment on a Loan To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay? To buy a laptop computer, Elaine borrowed $2,000 for 3 years at an annual simple interest rate of 5%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay? 16

17 Examples: Determining the Amount of Investment Time Nancy invested $6,000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested? TJ invested $4,000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested? Examples: Computing Total Savings John s parents deposited $1,000 into a savings account as a college fund when he was born. How much will he have in his account after 18 years at a yearly simple interest rate of 3.25%? Bertha deposited $1,000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%? 17

18 Examples: Finding the Rate of Interest Mr. Johnson borrowed $8,000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money? Mr. Mogi borrowed $9,000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money? 18